Arithmeticorum libri duo

Maurolicus, F. (1575). Arithmeticorum libri duo.

Type

Book

Intellectual base

Review or monograph

Year

1575

Link

no authoritative link yet

Cited from

mathematics

Cited by

1 citation across 1 artifact.

Primes

• Mathematical Induction
  • Mathematical induction is the local-to-global proof-propagation principle that: (1) a statement about all elements of a well-founded domain (typically the natural numbers) is proved by proving it for a base case and proving that its truth for an element implies its truth for the successor — formally, to prove \(\forall n \in \mathbb{N}, P(n)\): show \(P(0)\) (base case), and show \(\forall n: (P(n) \Rightarrow P(n+1))\) (inductive step); the conclusion \(\forall n, P(n)\) then follows from the well-foundedness of \(\mathbb{N}\) — every natural number is reached by finitely many successor steps from $0$, so the base plus step cover all cases via the well-ordering principle of \(\mathbb{N}\); this principle was made explicit by Maurolicus

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